Question: Which of the following numbers is a factor of 117? ${2,5,7,9,11}$
By definition, a factor of a number will divide evenly into that number. We can start by dividing $117$ by each of our answer choices. $117 \div 2 = 58\text{ R }1$ $117 \div 5 = 23\text{ R }2$ $117 \div 7 = 16\text{ R }5$ $117 \div 9 = 13$ $117 \div 11 = 10\text{ R }7$ The only answer choice that divides into $117$ with no remainder is $9$ $ 13$ $9$ $117$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $9$ are contained within the prime factors of $117$ $117 = 3\times3\times13 9 = 3\times3$ Therefore the only factor of $117$ out of our choices is $9$. We can say that $117$ is divisible by $9$.